Fixed arithmetic pipelines, Computer Engineering

Fixed Arithmetic pipelines

We obtain the example of multiplication of fixed numbers. The Two fixed-point numbers are added by the ALU using shift and add operations. This sequential implementation makes the multiplication a slow process. If we seem at the multiplication process cautiously, then we examine that this is the process of adding the multiple copies of shifted multiplicands as given below:

Now, we can signify the following phases for the pipeline:

The first stage produces the partial product of the numbers, which shows the six rows of shifted multiplicands.

In the second phase, the six numbers are given to the two CSAs merging into four numbers.

In the third stage, there is a one CSA merging the numbers into 3 numbers.

In the fourth stage, there is a one number merging three numbers into 2 numbers.

In the fifth stage, the final two numbers are added through a CPA to get the last product.

These phases have been implemented using CSA tree as shown in Figure:-